Relevance of instrumented gait analysis in the prediction of the rebound phenomenon after guided growth intervention

Predictors of rebound after correction of coronal plane deformities using temporary hemiepiphysiodesis (TH) are not well defined. The following research questions were tested: (1) Is the dynamic knee joint load useful to improve rebound prediction accuracy? (2) Does a large initial deformity play a critical role in rebound development? (3) Are BMI and a young age risk factors for rebound? Fifty children and adolescents with idiopathic knee valgus malalignment were included. A deviation of the mechanical femorotibial angle (MFA) of ≥ 3° into valgus between explantation and the one-year follow-up period was chosen to classify a rebound. A rebound was detected in 22 of the 50 patients (44%). Two predictors of rebound were identified: 1. reduced peak lateral knee joint contact force in the first half of the stance phase at the time of explantation (72.7% prediction); 2. minor initial deformity according to the MFA (70.5% prediction). The best prediction (75%) was obtained by including both parameters in the binary logistic regression method. A TH should not be advised in patients with a minor initial deformity of the leg axis. Dynamic knee joint loading using gait analysis and musculoskeletal modeling can be used to determine the optimum time to remove the plates.

www.nature.com/scientificreports/initial deformities 5 , higher 6 or lower body mass index (BMI) 7 in patients with idiopathic valgus malalignment.Moreover, young age at the beginning of treatment with substantial remaining growth potential after implant removal is most frequently reported in the literature [5][6][7][8] .However, after growth termination in adulthood, recurrence of the initial deformity can occur after axis correction following high tibial osteotomy 9 .Thus, the presence of residual growth after implant removal cannot be the only factor for recurrence, which necessitates the exploration of other predictors.
The mechanical load at the knee joint during gait can affect the development of the leg axis 10,11 .According to the Hueter-Volkmann law 12 , unilateral changes in compressive forces cause asymmetrical growth of a joint.The chondral modeling theory 10 suggests that physiological loading stimulates growth, while loads outside this range, either higher or lower, will lead to suppression.Instrumented gait analysis, in combination with musculoskeletal (MSK) modeling, can be used as an indirect method to assess the dynamic knee joint loading.The external knee adduction moment (KAM) is the most used measure of joint loading and has an important relationship with the initiation and progression of knee osteoarthritis (OA) 13,14 .MSK modeling can reveal compressive forces in the lateral and medial compartments, which may be closer to the actual forces acting at the knee joint 15 .
The objective of the present prospective study was to identify predictors of rebound at the time of implantation and explantation of the plates in a homogeneous group of children and adolescents with idiopathic knee valgus malalignment following a TH.In particular, we primarily performed this study to answer the following questions: (1) Is the mechanical load at the knee joint during gait useful to improve rebound prediction accuracy?(2) Does a large initial deformity play a critical role in rebound development?(3) Are BMI and a young age at the beginning of treatment with substantial remaining growth potential after implant removal risk factors for the occurrence of rebound?

Radiological examination
Considering the initial deformity, both the radiographic MAD (p = 0.011) and MFA (p = 0.006) were significantly more pronounced in the group without an occurrence of rebound phenomenon.In contrast, no significant group differences were detected in radiographic parameters at the time of explantation (Table 1).
The MFA in the rebound group increased from − 5.1 ± 1.7° valgus malalignment at the time of implantation to a neutral alignment of 0.6 ± 1.8° at the time of explantation and decreased again to − 3.3 ± 1.6° valgus malalignment at the one-year follow-up (Fig. 1).

Kinematics and mechanical load at the knee joint during gait
Of the 50 included patients, 22 developed a rebound at the one-year follow-up period after implant removal, indicating a rebound rate of 44%.The three groups did not show any significant differences in spatiotemporal kinematic gait parameters (e.g., walking speed) neither at the time of implantation nor at the time of explantation (Table 2).At the time of implantation, the external KAMs (both peaks and impulse) were significantly lower in the no rebound group compared to controls.No significant differences were detected between the rebound group and controls.The peak medial knee joint contact forces were significantly lower in both patient groups compared to controls.The peak lateral knee joint contact forces were significantly higher in the no rebound group compared to the rebound group and controls (Table 2).
At the time of explantation, the external KAM2 and the KAM impulse were significantly higher in both patient groups compared to controls.The peak medial knee joint contact forces did not show any significant group differences.In contrast, the peak lateral knee joint contact force in the first half of the stance phase was significantly lower in the rebound group compared to the no rebound group and controls.The peak lateral knee joint contact force in the second half of the stance phase was significantly lower in both patient groups compared to controls (Table 2).
For the binary logistic regression analysis (Table 3), only independent variables, available at the time of implantation or explantation, that allowed significant differentiation between groups (no rebound, rebound) based on the aforementioned analyses were included.The two most important predictors for rebound were as follows: 1. reduced peak lateral knee joint contact force in the first half of the stance phase at the time of explantation (model 1, 72.7% accurate prediction); 2. minor initial deformity according to the MFA (model 2, 70.5% accurate prediction).A stepwise forward method of regression (likelihood ratio method) including both variables slightly but significantly increased the prediction accuracy to 75.0% (model 3).The addition of the variables peak lateral knee joint contact force during the first and second half of the stance phase at the time of implantation, as well as age and BMI (implantation and explantation) did not significantly improve prediction accuracy of this model.Other potential predictors (indicating significant differences between no rebound and rebound) showed high collinearity with the included variables (MAD with MFA: r = 0.927, p < 0.001), or were not available at the time of implantation or explantation (residual growth from the time of explantation to the one-year follow-up).

Study population characteristics
There were no significant differences in age, body height, and BMI among the two patient groups at the time of implantation and explantation.In contrast, the residual growth (change in body height) from the time of explantation to the one-year follow-up was significantly higher (p = 0.009) in the rebound group (Table 1).
More male (66%) than female (34%) patients were included in this study.However, there were no sex differences between the two groups (no rebound, rebound, p = 0.797) (Table 1).In 35 of 50 patients (70%) plates were implanted on the medial distal femur, in 7 patients (14%) on the medial proximal tibia, and in 8 patients (16%) on the medial distal femur and the medial proximal tibia.There was no significant difference in the distribution of implant localization between these two patient groups (p = 0.347) (Table 1).The average implantation period was 12.1 ± 5.1 months in the group without a rebound and 9.9 ± 2.4 months in the rebound group, without any significant difference (p = 0.068).The longitudinal change of body height between implantation and explantation of the plates was also not significantly different between both groups (p = 0.818) (Table 1).
The three groups did not show any significant differences in sex and age neither at the time of implantation nor at the time of explantation (Table 2).At both times, BMI was significantly higher in both patient groups compared to controls, and controls had a significantly shorter body height than the no rebound group.The non-invasive marker-based MFA calculated using the static gait analysis trial did not show significant group differences or pathological values at the time of explantation (Table 2).

Discussion
The high rebound rate of 44% is in accordance with the study of Ko et al. 16 .(42.6% rebound rate) and clearly highlights a clinical problem after initial successful TH in children and adolescents with idiopathic knee valgus malalignment that has to be seriously considered and to be explained to the parents.In the present study, we focused on predictors that are available at the time just before a possible implantation or explantation and thus may influence the indication for a TH, or the timing of implant removal.Two crucial predictors of rebound were identified: 1. reduced peak lateral knee joint contact force in the first half of the stance phase at the time of explantation; 2. minor initial deformity according to the MFA.The best rebound prediction (75.0%) was obtained by including both parameters in the regression method.In contrast, age and BMI did not play a critical role in rebound development.

Influence of dynamic knee joint loading on rebound prediction
The mechanical load at the knee joint during gait can affect the development of the leg axis 10,11 .The KAM is a commonly used surrogate measure for medial compartment knee loading because it is statistically associated with OA initiation and progression 13,14 .Although conventional knee joint moments during gait did not play a critical role as rebound predictor in our patient group, they can be used as a decision criterion for the indication of TH 17 .In particular, the indication for a TH should be considered when the knee joint moments in the Table 1.Group differences (no rebound, rebound) in study population characteristics and radiographic parameters (n = 50) at the time of implantation and explantation of the plates.Normally distributed data: Mean with standard deviation in parenthesis.*Not normally distributed data: Median with interquartile range in parenthesis.MAD: mechanical axis deviation, medial deviation (varus) is depicted as positive and lateral deviation (valgus) as negative values; MFA: mechanical femorotibial angle, varus malalignment is depicted as positive angles and valgus malalignment as negative angles.Significant differences are bold printed.frontal plane are significantly lower compared to healthy controls at the same age.This was only the case in the patient group without a rebound incident (Table 2).In contrast, patients with frontal plane knee joint moments that were only slightly and not significantly different compared to controls (rebound group) appeared to be at increased risk for a rebound.In clinical practice, a pathological joint load is assumed if the deviation of the knee joint moments in the frontal plane exceeds one times the standard deviation of an age-matched reference group 17 .
Calculating joint contact forces requires additional use of musculoskeletal simulation software (e.g., Open-Sim).Joint contact forces are part of the internal load and are mainly generated by muscles during walking 18,19 and thus may be more representative of cartilage loading 20 .At the time of explantation, the peak lateral knee joint contact force in the first half of the stance phase was significantly reduced in patients with a rebound incident compared to patients with no rebound incident and controls in the present study.The exact mechanisms by which growth plate responds to mechanical loading remain largely unclear 21 , although systemic, local, and mechanical factors play a role 22 .Mechanically, mild tension and compression encourage longitudinal bone growth, whereas compression loads above or below a certain threshold inhibit longitudinal bone growth 10 .Therefore, bone growth has a nonlinear relationship with mechanical loading.When this is applied to our results, it may be assumed that the pathological reduction of the peak lateral knee joint contact force in the rebound group led to growth inhibition in the lateral part of the growth plate, resulting in a recurrent genu valgum deformity.In contrast, the peak medial knee joint contact forces were not significantly different between the groups and could therefore be considered physiological, which is related to normal bone growth in the medial part of the growth plate.Therefore, in our opinion, this incongruity in the knee joint at possible explantation can contribute to the development of a rebound.These group differences could not be attributed to the effect of sex, age, walking speed, or other spatiotemporal gait parameters, as no differences between groups exist in these parameters.In addition, the static leg axis parameters (MAD and MFA) did not show significant group differences or pathological values at the time of explantation.This further indicates firstly, the plates were removed when the leg axis was aligned (no overcorrection were performed), and secondly, the control group did not present leg axis deformities.
Some authors have recommended overcorrection to overcome the rebound phenomenon, without suggesting a specific procedure 23,24 .Our study provides evidence that patients with a pathological reduction of peak lateral knee joint contact force at the time of possible explantation may benefit from this strategy, but it remains controversial as there are no established guidelines for the amount of overcorrection to be performed 5 .Therefore, it is recommended that the amount of overcorrection should be limited to achieve acceptable alignment without causing an opposing deformity (genu varum).Additionally, it is still unclear whether overcorrection can prevent deformity recurrence.

Influence of static leg axis alignment on rebound prediction
Unlike the study by Leveille et al. 5 , a more severe preoperative deformity was not a risk factor for rebound in our study.However, the deformities in that study were pronounced (> 20° mechanical axis deviation from neutral) and cannot be compared directly with our patient group.Zaidman et al. 25 also did not find a positive correlation between the magnitude of initial deformity and rebound.The results of the present study suggest that a  www.nature.com/scientificreports/dynamic frontal plane knee joint moments in the group with a rebound incident.Considering the high rebound rate in patients with idiopathic knee valgus malalignment, we recommend the indication for a TH when the axial malalignment (MFA) exceeds 5°, and/or the MAD falls within zone 2 or 3 according to the classification originally developed by Müller and Müller-Färber 26 .Additionally, for unclear or borderline cases with marginal deviations in MAD (zones 1 and 2) and MFA, instrumented gait analysis and the determination of dynamic knee joint loading 17,27 should be included to determine whether surgical treatment is necessary.

Influence of anthropometric parameters on rebound prediction
In the field of academic writing, a common risk factor for rebound is a young age at the beginning of treatment with high remaining growth potential after implant removal [5][6][7][8] .Although age difference between groups was not significant in our study, the residual growth from implant removal to the one-year follow-up was significantly higher in the rebound group.Therefore, accurately estimating skeletal maturity and predicting residual growth are crucial for determining the optimal timing for growth-guiding interventions.Various methods exist for determining remaining growth potential and optimal timing for epiphysiodesis procedures, but their accuracy is discussed controversially, and their applicability in specific patient populations has not been extensively studied [28][29][30] .Additionally, the presence of residual growth alone is not the only factor the determines the possibility of rebound, as recurrence of the initial deformity can occur in adulthood after axis correction following high tibial osteotomy 9 .Based on our homogeneous patient group with idiopathic knee valgus malalignment, a higher 6 or lower 7 BMI did not play a critical role in the development of a rebound.However, both patient groups showed a significantly higher BMI compared to healthy controls at the same age.As the calculation of the dynamic joint loading was normalized to body mass in the present study, this difference has no influence on our gait analysis results.A strong association between higher BMI and knee valgus malalignment has previously been shown 31,32 .

Limitations
The results of the present study should be interpreted in the light of its limitations.First, although the dynamic knee joint moments and contact forces are validated mathematical calculations of the mechanical loading of the knee joint, they do not investigate how these global loads translate into soft tissue loads in the growth plate.In a further methodological step, the finite element method could provide a deeper understanding of locally varying mechanical loading of tissue regions with complex, irregular geometries and their dependency on external loads and boundary conditions.Using the finite element method, it is possible to investigate how tension-band plates change the distribution, type, and size of mechanical stresses in juvenile growth plates 33 .Second, we included more male (66%) than female (34%) participants.Although we did not detect significant differences in sex between groups, potential differences in sex regarding rebound prediction should be investigated in a larger study population with a balanced proportion of female and male participants.

Conclusion
In conclusion, a substantial rebound rate of 44% following successful surgery with TH in children and adolescents with idiopathic knee valgus malalignment highlights the importance of regular follow-up for these patients, ideally until skeletal maturity.To minimize radiation exposure during examinations, a non-invasive markerbased approach using instrumented gait analysis can be considered if available 34 .This study identified two key predictors of the rebound phenomenon: 1. reduced peak lateral knee joint contact force in the first half of the Table 3. Binary logistic regression analysis.A stepwise forward method of regression (likelihood ratio method) was performed in all 50 patients.The following predictor variables that allowed a significant differentiation between groups (no rebound, rebound) were included: 1. peak lateral knee joint contact force during the first half of the stance phase at the time of explantation (latKCF1_expl); 2. mechanical femorotibial angle at the time of implantation of the plates (MFA_impl).The variable peak lateral knee joint contact force during the first half of the stance phase at the time of implantation did not significantly improve prediction accuracy of model 3. Model 1 with latKCF1_expl as included variable: R 2   www.nature.com/scientificreports/stance phase at the time of explantation (72.7% prediction); 2. minor initial deformity with an MFA of approximately 5° or less (70.5% prediction).The best prediction (75%) was obtained by incorporating both parameters in the regression method.This is the first study emphasizing the importance of the dynamic load situation at the knee joint for optimized treatment of children and adolescents with idiopathic knee valgus malalignment.A TH should not be recommended for patients with physiological frontal plane knee joint moments and a minor deformity of the leg axis.At the time of possible explantation, instrumented gait analysis in combination with MSK modeling can be used to determine whether the plates should be removed or remain in the joint to achieve a slight overcorrection.

Participants/study design
In this prospective cohort study (level of evidence: III), 50 children and adolescents with idiopathic knee valgus malalignment without other orthopedic comorbidities and an indication for TH were evaluated at three different time points (a few days before implantation, a few days before explantation, and one year after removal of the plates) between August 2018 and July 2023 (Table 1).The indication for TH was set for skeletally immature patients with a pathological idiopathic valgus alignment deformity (mechanical axis deviation (MAD) of > 10 mm lateral and/or mechanical femorotibial angle (MFA) of > 3° valgus) of one or both lower extremities based on a full-length standing anteroposterior radiograph 35 .The decision for implant insertion in the femur, tibia, or both segments was made according to pathological joint surface angles: mechanical lateral distal femur angle (mLDFA) and mechanical medial proximal tibia angle (mMPTA) (physiological values for mLDFA 88 ± 2.5° and for mMPTA 87 ± 2.5°) 36 .In the case of bilateral involvement, only the more severely affected leg was analyzed.Either Eight-Plates (Orthofix, Lewisville, TX, USA) or Pedi-Plates (Orthopediatrics Inc., Warsaw, IN, USA) were used as implant.A deviation of the MFA of ≥ 3° into valgus between explantation and the one-year follow-up period was chosen to classify a rebound 7,16 .This means, if the MFA increased by ≥ 3° into valgus (independent of the absolute value of the leg axis), it is assumed as rebound.A one-year follow-up period was chosen because a temporary over-activation of growth has been observed for a period between eight to ten months following implant removal 37 .In addition, it has been shown that recurrence of deformity typically occurred within one year after plate removal 38 .Patients were excluded if they had rheumatoid arthritis, neuromuscular disorders, bony displasias, sagittal or transverse plane deformities of the leg tested by clinical examination, leg length discrepancy of more than 1 cm, clubfoot, flatfoot deformity receiving corrective surgery, history of major trauma of the lower extremity.Fifteen typically developing, healthy children and adolescents at the same age were recruited as control group for the gait analysis data (Table 2).Only one leg was randomly chosen to be included in the analyses.None of the enrolled individuals reported ankle, knee, hip, or back pain that required treatment at the time of measurements.All participants and their parents were familiarized with the study protocol.The participants and their parents provided written informed consent to participate in this study, as approved by the local ethics committee of the Faculty of Medicine at the Goethe University Frankfurt/Main (number: 182/16) and in accordance with the Helsinki Declaration.This study was first registered in the German Clinical Trials Register (DRKS) (number: DRKS00010296) on 21/04/2016.

Radiographic evaluations
MAD and MFA were determined on a full-length standing anteroposterior radiograph with TraumaCad® (version 2.3.4.1, Voyant Health, Petach-Tikva, Israel).The criteria for a valid radiographic image were: patient standing in a weight-bearing position, both legs parallel to each other and shoulder-width apart, fully extended knees, and patella centered over the femoral condyles pointing straight forward to avoid rotational errors 39 .
The malalignment analysis was performed following the principles described by Paley et al. 36 .The MFA was defined as the angle formed by the line from the center of the hip to the center of the knee (mechanical femur line) and the line from the center of the knee to the center of the ankle (mechanical tibia line) 40 .The center of the hip joint was determined by drawing a best-fitting circle around the head of the femur using the tools provided in TraumaCad®.The center of the knee joint was defined as the midpoint between the center of the intercondylar region and the center of the eminentia intercondylaris.The center of the ankle was defined as the midpoint of the tibial articular surface of the talus.Neutral alignment was defined as 0°, varus malalignment as positive angle, and valgus malalignment as negative angle.

Gait analysis methods
Kinematic data were collected at 200 Hz using an 8-camera motion capture system (MX T10, VICON Motion Systems, Oxford, UK).Ground reaction forces were recorded at 1000 Hz using two force plates (Advanced Mechanical Technology, Inc., Watertown, MA, USA) embedded at the midpoint of a 15 m long level walkway.For each subject and time point, a series of five barefoot walking trials at a self-selected speed were averaged for further analysis on the basis of complete marker trajectories and a clear foot-forceplate contact.For enhanced reliability and accuracy, a lower body protocol (MA), described in a previous investigation, was used 42 .In addition to the standardized Plug-in-Gait marker set 43 , reflective markers on the medial malleolus, medial femoral condyle, and greater trochanter were used to determine the centers of rotation for the ankle, knee, and hip joints.
The centers of rotation for the ankle and knee joints were defined statically as the midpoints between the medial and lateral malleolus and femoral condyle markers.The center of the hip joint was calculated using a standardized geometrical prediction method using regression equations 44 .
External knee joint moments (normalized to body mass) were determined using an inverse dynamics approach 44 .The distinctive "m" or "double hump" shape of the external knee adduction moment (KAM) waveform in the frontal plane has led researchers to report several discrete variables related to it 15,45 .Therefore, the first (KAM1) and second peaks (KAM2) of the knee adduction moment in loading response/mid stance and terminal stance were analyzed.In addition, the impulse of the KAM (area under the curve) 46 was calculated.To account for possible differences in leg length, walking speed and step length were normalized to leg length according to Hof 47 .

Musculoskeletal modeling
Input from marker positions and ground reaction forces were prepared using the MOtoNMS toolbox (version 3) in MATLAB (2020b, The MathWorks, Inc., Natick, MA, USA) for use in OpenSim (4.1) 48.Force data were filtered using a zero-lag low-pass Butterworth filter with a cut-off frequency of 10 Hz.An OpenSim model 18 with 20 degrees of freedom was used.The knee joint had sagittal and frontal-plane rotational degrees of freedom, and the medial and lateral contact forces were resolved using a multi-compartment knee model 19,49 .We further personalized the models by adjusting the frontal-plane alignment with the MFA measured from X-ray images 19 .X-rays were not available for the control group, and the MFA was calculated using a static gait analysis trial 27,34 .This non-invasive marker-based approach correlates well with the determination of lower limb alignment in the frontal plane using radiographs in young patients with varus or valgus malalignment 34 .Peak knee contact forces in loading response/mid stance and terminal stance were normalized by body mass and computed as the reaction force in the medial and lateral compartments of the knee in the direction of the long axis of the tibia 27,50 .

Statistical analysis
Statistical analyses were performed using SPSS Statistics (version 29, IBM Corporation, New York, NY, USA).The Shapiro-Wilk test was used to verify normal distribution.All variables were normally distributed, except residual growth from the time of explantation to the one-year follow-up, BMI and step width at the time of implantation and explantation, as well as the following variables at the time of implantation: peak KAM in the first half of the stance phase, and peak medial knee joint contact forces in the first and second half of the stance phase.
Differences in anthropometric and clinical data between both patient groups (no rebound, rebound) were tested for significance using an unpaired, two-tailed Student's t-test for normally distributed data and a Mann-Whitney U-test for non-normally distributed data.A chi-squared test was used to compare the sex distribution and the implant localization between groups.
Group differences (no rebound, rebound, controls) including gait data were derived from one-way ANOVA for normally distributed data.In case of significance, unpaired two-tailed post-hoc t-tests with Bonferroni correction were performed to control for type 1 errors.A Kruskal-Wallis test following a Mann-Whitney post-hoc test in case of significance were used for not normally distributed data.
A binary logistic regression analysis was performed to determine predictor variables that best explained the rebound phenomenon.In particular, a stepwise forward method of regression (likelihood ratio method) was performed by setting the occurrence (yes or no) of the rebound phenomenon as a dependent variable.For this purpose, only independent variables that allow a significant differentiation between groups (no rebound, rebound) at the time of implantation and explantation based on the previously described analysis above were included.Multicollinearity (r > 0.7) between potential predictor variables was excluded 51 .The significance level was set at p ≤ 0.05.

Figure 1 .
Figure 1.Mean and standard deviation of the mechanical femorotibial angle (MFA) changes over time of the rebound group (n = 22).

Table 2 .
34oup differences (no rebound, rebound, controls) in study population characteristics and gait parameters at the time of implantation and explantation of the plates.Normally distributed data: Mean with standard deviation in parenthesis.*Notnormallydistributed data: Median with interquartile range in parenthesis.MFA: mechanical femorotibial angle (non-invasive marker-based approach34), varus malalignment is depicted as positive angles and valgus malalignment as negative angles.Significant values are in bold.